Calculate Rectangle Perimeter: Triangle Perimeter = 20 with Side X+2

Q: Why do I need to use the triangle perimeter first?

The triangle perimeter gives you the constraint equation to find x! Without solving $ 20 = 10 + 6 + (x+2) $, you can't determine the actual lengths of the rectangle sides.

Q: How do I know which sides belong to the triangle BCD?

Look at the diagram carefully! Triangle BCD uses the diagonal (length 10), one width (length 6), and one height (length x+2). These three sides must add up to 20.

Q: Why does the rectangle have two different side lengths?

A rectangle has opposite sides equal. Here, the width is 6 and height is x+2 = 4, so perimeter = $ 2(6) + 2(4) = 20 $.

Q: What if I get confused about which measurement goes where?

Use the vertex labels! Triangle BCD connects points B, C, and D. From the diagram, identify: BC = x+2, CD = 6, and diagonal BD = 10.

Q: How can I check if my rectangle perimeter is correct?

Add all four sides: $ AB + BC + CD + DA $. Since opposite sides are equal in a rectangle, this becomes $ 2(length) + 2(width) $. For this problem: $ 2(4) + 2(6) = 20 $ ✓

Rectangle Perimeter with Triangle Constraint

Look at the following rectangle:

Given that the perimeter of the triangle BCD is 20, what is the perimeter of the rectangle ABCD?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's begin by finding the perimeter of the rectangle.

00:13 To find a triangle's perimeter, add up the lengths of all its sides.

00:24 Now, plug in the given values to solve for X. Take your time.

00:41 Great job! Now gather all similar terms together.

00:48 Let's focus on getting X alone on one side of the equation.

00:53 You found the value of X! Next, use this to find the side length.

01:03 Remember, opposite sides in a rectangle are equal.

01:18 To find the perimeter of the rectangle, add up all the sides.

01:23 Substitute in the values you have and calculate the perimeter.

01:42 And there you have it! That's your solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following rectangle:

Given that the perimeter of the triangle BCD is 20, what is the perimeter of the rectangle ABCD?

Step-by-step solution

Given that the perimeter of triangle BCD is 20

We can therefore insert the existing data and calculate as follows:

$20=10+6+x+2$

$20=16+x+2$

$20-16-2=x$

$x=2$

Now we can calculate the BC side: 2+2=4

Perimeter of the rectangle ABCD:

$6+6+4+4=12+8=20$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Triangle Perimeter: Add all three sides of triangle BCD to find unknown
Solve Variable: From 20 = 10 + 6 + (x+2), get x = 2
Rectangle Check: Opposite sides equal: AB = DC = 4, AD = BC = 6 ✓

Common Mistakes

Avoid these frequent errors

Adding rectangle sides directly without finding x
Don't add 10 + 6 + (x+2) + unknown side = wrong calculation! This skips the crucial step of finding x first. Always use the triangle perimeter constraint to solve for x, then calculate all rectangle sides.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to use the triangle perimeter first?

The triangle perimeter gives you the constraint equation to find x! Without solving $20 = 10 + 6 + (x+2)$ , you can't determine the actual lengths of the rectangle sides.

How do I know which sides belong to the triangle BCD?

Look at the diagram carefully! Triangle BCD uses the diagonal (length 10), one width (length 6), and one height (length x+2). These three sides must add up to 20.

Why does the rectangle have two different side lengths?

A rectangle has opposite sides equal. Here, the width is 6 and height is x+2 = 4, so perimeter = $2(6) + 2(4) = 20$ .

What if I get confused about which measurement goes where?

Use the vertex labels! Triangle BCD connects points B, C, and D. From the diagram, identify: BC = x+2, CD = 6, and diagonal BD = 10.

How can I check if my rectangle perimeter is correct?

Add all four sides: $AB + BC + CD + DA$ . Since opposite sides are equal in a rectangle, this becomes $2(length) + 2(width)$ . For this problem: $2(4) + 2(6) = 20$ ✓

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